Consider a set of options: 7 possible candidates for an executive office, 15 different
variants of a bill, in fact any set of any number of possibilities. Now imagine a voter considering those
options. The voter is free to consider any or all of those options. To “consider” an option is to cast a vote for it in
the unit interval.
The option with the highest final value () wins (if you need 5 out of
42, the top 5 win). Here is how we calculate that final value:

The purpose of the unit-circle function is to attenuate as
approaches 0. Note that because a linear function in the same position attenuates
more severely, a vote of 0 is always stronger disapproval than unconsidered (at the two edge
cases it may look equal, but at one edge there are no considered and at the other no unconsidered, eliminating comparison):